Neutron-Antineutron Oscillation, Low-scale Baryogenesis, Dark Matter - - PowerPoint PPT Presentation

Neutron-Antineutron Oscillation, Low-scale Baryogenesis, Dark Matter and LHC Physics

BHUPAL DEV

Washington University in St. Louis

• R. Allahverdi, BD and B. Dutta, arXiv:1711.xxxxx.

BD and R. N. Mohapatra, Phys. Rev. D 92, 016007 (2015) [arXiv:1504.07196].

INT Workshop on Neutron-Antineutron Oscillations University of Washington, Seattle

October 26, 2017

Proton Decay vs n − ¯ n

Selection rules for ∆B ∆B = 1 Proton decay Induced by dimension-6 operator (also dimension-5 in SUSY). Amplitude ∝ Λ−2. τp 1034 yr implies Λ 1015 GeV. Proton decay requires GUT-scale physics. ∆B = 2 Di-nucleon decay and n − ¯ n Induced by dimension-9 operator. Amplitude ∝ Λ−5. Λ 100 TeV enough to satisfy experimental constraints. n − ¯ n oscillation could come from a TeV-scale new physics. ∆B = 0 could be linked to baryogenesis (Sakharov).

Highlights of this Talk

A simple TeV-scale SM-extension with baryogenesis, dark matter and n − ¯ n. Introduces / B-interactions via TeV-scale color-triplet scalars (Xα) and a singlet Majorana fermion (ψ) that couple only to the RH quarks. ψ is stable, and hence, a DM candidate, if mψ ≃ mp. Baryogenesis occurs via out-of-equilibrium decays of Xα. Common origin for both baryon and DM abundance. Requirements of successful baryogenesis and ΩDM/Ωb ≈ 5 put meaningful constraints on the model parameter space. Observable n − ¯ n in the allowed parameter space. Complementarity with monojet/monotop signals at the LHC.

Highlights of this Talk

A simple TeV-scale SM-extension with baryogenesis, dark matter and n − ¯ n. Introduces / B-interactions via TeV-scale color-triplet scalars (Xα) and a singlet Majorana fermion (ψ) that couple only to the RH quarks. ψ is stable, and hence, a DM candidate, if mψ ≃ mp. Baryogenesis occurs via out-of-equilibrium decays of Xα. Common origin for both baryon and DM abundance. Requirements of successful baryogenesis and ΩDM/Ωb ≈ 5 put meaningful constraints on the model parameter space. Observable n − ¯ n in the allowed parameter space. Complementarity with monojet/monotop signals at the LHC.

The Model

Start with the SM gauge group and add renormalizable terms that violate baryon number. Gauge invariance requires introduction of new colored fields. A minimal setup: Iso-singlet, color-triplet scalars Xα with Y = +4/3. Allows Xαdcdc terms in the Lagrangian. Need at least two (α = 1, 2) to produce baryon asymmetry from X decay. Total baryon asymmetry vanishes after summing over all flavors of dc.

[Kolb, Wolfram (NPB ’80)]

Need additional / B interactions. Introduce a SM-singlet Majorana fermion ψ (also plays the role of DM). L ⊃

• λαiX∗

αψuc i + λ′ αijXαdc i dc j + 1

2mψ ¯ ψcψ + H.c.

• .

[Allahverdi, Dutta (PRD ’13); BD, Mohapatra (PRD ’15); Davoudiasl, Zhang (PRD ’15)]

The Model

Start with the SM gauge group and add renormalizable terms that violate baryon number. Gauge invariance requires introduction of new colored fields. A minimal setup: Iso-singlet, color-triplet scalars Xα with Y = +4/3. Allows Xαdcdc terms in the Lagrangian. Need at least two (α = 1, 2) to produce baryon asymmetry from X decay. Total baryon asymmetry vanishes after summing over all flavors of dc.

[Kolb, Wolfram (NPB ’80)]

Need additional / B interactions. Introduce a SM-singlet Majorana fermion ψ (also plays the role of DM). L ⊃

• λαiX∗

αψuc i + λ′ αijXαdc i dc j + 1

2mψ ¯ ψcψ + H.c.

• .

[Allahverdi, Dutta (PRD ’13); BD, Mohapatra (PRD ’15); Davoudiasl, Zhang (PRD ’15)]

Dark Matter

Integrate out Xα to obtain ψuc

i dc j dc k interaction (assuming mψ ≪ mX).

ψ decays to three quarks (baryons) if mψ ≫ GeV. Also ψ → p + e− + ¯ νe if mψ > mp + me. Absolutely stable for mψ < mp + me (no discrete symmetry required). In addition, need mp > mψ + me to avoid p → ψ + e+ + νe. So the viable scenario for ψ to be the DM candidate is (see also A. Nelson’s talk) mp − me ≤ mψ ≤ mp + me . ψ cannot give mass to light neutrinos through HψL term, because this with Xψuc and Xdcdc terms will induce the dimension-7 operator HLucdcdc for rapid proton decay. Stability of DM is linked to the stability of proton.

Dark Matter

Integrate out Xα to obtain ψuc

i dc j dc k interaction (assuming mψ ≪ mX).

ψ decays to three quarks (baryons) if mψ ≫ GeV. Also ψ → p + e− + ¯ νe if mψ > mp + me. Absolutely stable for mψ < mp + me (no discrete symmetry required). In addition, need mp > mψ + me to avoid p → ψ + e+ + νe. So the viable scenario for ψ to be the DM candidate is (see also A. Nelson’s talk) mp − me ≤ mψ ≤ mp + me . ψ cannot give mass to light neutrinos through HψL term, because this with Xψuc and Xdcdc terms will induce the dimension-7 operator HLucdcdc for rapid proton decay. Stability of DM is linked to the stability of proton.

DM Relic Density

For mψ ≈ mp, only annihilation channel is ψψ → ucuc. σannv ∼ |λα1|4m2

ψ

8πm4

X

. For mX ∼ O(1 TeV), even λ ∼ O(1) gives σannv ≪ 3 × 10−26 cm3s−1. Thermal overproduction of ψ (as expected). [Lee, Weinberg (PRL ’77]] Need a non-thermal mechanism to obtain the correct relic density. Late decay of a scalar (moduli) field φ with a low reheating temperature TR ≤ GeV. [Moroi, Randall (NPB ’00); Allahverdi, Dutta, Sinha (PRD ’10)] nψ s = YφBrφ→ψ , where Yφ = 3TR

4mφ is the entropy dilution due to the φ decay.

DM Relic Density

For mψ ≈ mp, only annihilation channel is ψψ → ucuc. σannv ∼ |λα1|4m2

ψ

8πm4

X

. For mX ∼ O(1 TeV), even λ ∼ O(1) gives σannv ≪ 3 × 10−26 cm3s−1. Thermal overproduction of ψ (as expected). [Lee, Weinberg (PRL ’77]] Need a non-thermal mechanism to obtain the correct relic density. Late decay of a scalar (moduli) field φ with a low reheating temperature TR ≤ GeV. [Moroi, Randall (NPB ’00); Allahverdi, Dutta, Sinha (PRD ’10)] nψ s = YφBrφ→ψ , where Yφ = 3TR

4mφ is the entropy dilution due to the φ decay.

Baryogenesis

Via direct decays of Xα → ψuc

i , dc i dc j .

Independent of sphaleron processes. Example of post-sphaleron baryogenesis. [Babu, Mohapatra, Nasri (PRL ’06)] For complex λαi or λ′

αij, interference of tree and one-loop contributions

produces a non-zero CP asymmetry. In principle, either self-energy or vertex diagrams or both could contribute. In the non-thermal scenario, final baryon asymmetry also depends on the moduli decay rate: ηB ≃ 7.04 Yφ

• α

Brφ→Xαǫα .

Moduli Decay

Naturally long-lived due to gravitationally suppressed couplings. Dominates the energy density of the universe before decaying. Must decay well before BBN (TBBN ∼ MeV). Decay rate: Γφ = cφ

2π m3

φ

M2

Pl , where cφ ∼ 0.01 − 1 (in typical string

compactification scenarios, e.g. KKLT). Moduli decay occurs when Γφ ∼ H ≃ 1.66√g∗ T2

MPl .

Reheat temperature: TR ≃ c1/2

φ

10.75 g∗ 1/4 mφ 100 TeV 3/2 3.5 MeV . Requiring MeV TR GeV implies 200 TeV mφ 4500 TeV, or 10−9 Yφ ≡ 3TR

4mφ 10−7.

Need ǫ ∼ 10−3 − 10−1.

Moduli Decay

Naturally long-lived due to gravitationally suppressed couplings. Dominates the energy density of the universe before decaying. Must decay well before BBN (TBBN ∼ MeV). Decay rate: Γφ = cφ

2π m3

φ

M2

Pl , where cφ ∼ 0.01 − 1 (in typical string

compactification scenarios, e.g. KKLT). Moduli decay occurs when Γφ ∼ H ≃ 1.66√g∗ T2

MPl .

Reheat temperature: TR ≃ c1/2

φ

10.75 g∗ 1/4 mφ 100 TeV 3/2 3.5 MeV . Requiring MeV TR GeV implies 200 TeV mφ 4500 TeV, or 10−9 Yφ ≡ 3TR

4mφ 10−7.

Need ǫ ∼ 10−3 − 10−1.

Resonant Baryogenesis

Similar in spirit to resonant leptogenesis. [Pilaftsis (PRD ’97); Pilaftsis, Underwood

(NPB ’03; PRD ’05); BD, Pilaftsis, Millington, Teresi (NPB ’14)]

Self-energy graphs dominate the CP-asymmetry for quasi-degenerate Xα’s. Resonantly enhanced [up to O(0.1)] for ∆mX ΓX/2. ǫα = 1 8π

• ijk Im(λ∗

αkλβkλ′∗ αijλ′ βij)

• k |λαk|2 +

ij |λ′ αij|2

(m2

Xα − m2 Xβ)mXαmXβ

(m2

Xα − m2 Xβ)2 + m2 XαΓ2 Xβ

In the resonance limit, regulator goes as mX/ΓX. CP-asymmetry becomes insensitive to the mass scale mX, as well as the

• verall scaling of the coupling constants.

Free Parameters and Constraints

Free parameters: mX, λαi, λ′

αij (with α = 1, 2 and i, j, k = 1, 2, 3).

Color antisymmetry requires that λ′

ij = 0 for i = j.

Similarly, color conservation does not allow tree-level contributions to quark FCNCs. Only major constraint comes from di-nucleon decay (like pp → KK): |λα1λ′

α12| 10−6(mX/1 TeV)2.

We assume λ′

12 small, while leave λα1 as a free parameter.

For simplicity, also assume |λ1i| = |λ2i| ≡ |λ| ∀ i = 1, 2, 3. Similarly, take |λ′

1ij| = |λ′ 2ij| ≡ |λ′ ij|.

Left with only four parameters mX, λ, λ′

13,23.

Free Parameters and Constraints

Free parameters: mX, λαi, λ′

αij (with α = 1, 2 and i, j, k = 1, 2, 3).

Color antisymmetry requires that λ′

ij = 0 for i = j.

Similarly, color conservation does not allow tree-level contributions to quark FCNCs. Only major constraint comes from di-nucleon decay (like pp → KK): |λα1λ′

α12| 10−6(mX/1 TeV)2.

We assume λ′

12 small, while leave λα1 as a free parameter.

For simplicity, also assume |λ1i| = |λ2i| ≡ |λ| ∀ i = 1, 2, 3. Similarly, take |λ′

1ij| = |λ′ 2ij| ≡ |λ′ ij|.

Left with only four parameters mX, λ, λ′

13,23.

DM-to-Baryon Ratio

Both DM and baryonic matter have a common origin from moduli decay. ΩDM Ωb = Brφ→ψ

• α ǫαBrφ→Xα

Brtotal

φ→ψ = Brdirect φ→ψ + α Brφ→XαBrXα→ψ ≥ α Brφ→XαBrXα→ψ.

This implies ΩDM

Ωb ≥ BrX→ψ ǫ

.

ΩDM Ωb ≈ 5 imposes an upper bound on the ratio |λ/λ′| 1/

√ 2, independent of mX, mφ.

0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4 5 6 7 8 |λ/λ'| ΩDM/Ωb

Baryon Asymmetry

0.0 0.2 0.4 0.6 0.8 1.0 0.001 0.010 0.100 1 |λ/λ'| Br(ϕ→X) ηB

• bs

ΩDM/Ωb

Puts a lower bound on |λ/λ′| and on the branching of moduli.

Baryon Asymmetry

0.0 0.2 0.4 0.6 0.8 1.0 0.001 0.010 0.100 1 |λ/λ'| Br(ϕ→X) ηB

• bs

ΩDM/Ωb

Puts a lower bound on |λ/λ′| and on the branching of moduli.

n − ¯ n Oscillation

Effective / B operator ψucdcdc (integrating out Xα). [Babu, Mohapatra, Nasri (PRL ’07)] Induces n − ¯ n oscillation for Majorana N. Tree-level amplitude vanishes due to color-antisymmetry. Non-zero amplitude at one-loop level: [BD, Mohapatra (PRD ’15)] Gn−¯

n ≃

1 16π2 |λα1|2|λ′

α13|4mψ

m6

Xα

log

• m2

Xα

m2

ψ

• ≃ (1.9 × 10−28 GeV−5)

|λα1| 0.03 2 |λ′

α13|

0.04 4 1 TeV mX 6 . Observable oscillation time for mX ∼ O(TeV): τn¯

n ≃ (3.0 × 108 sec)

0.03 |λα1| 2 0.04 |λ′

α13|

4 mX 1 TeV 6 .

n − ¯ n Oscillation

Effective / B operator ψucdcdc (integrating out Xα). [Babu, Mohapatra, Nasri (PRL ’07)] Induces n − ¯ n oscillation for Majorana N. Tree-level amplitude vanishes due to color-antisymmetry. Non-zero amplitude at one-loop level: [BD, Mohapatra (PRD ’15)] Gn−¯

n ≃

1 16π2 |λα1|2|λ′

α13|4mψ

m6

Xα

log

• m2

Xα

m2

ψ

• ≃ (1.9 × 10−28 GeV−5)

|λα1| 0.03 2 |λ′

α13|

0.04 4 1 TeV mX 6 . Observable oscillation time for mX ∼ O(TeV): τn¯

n ≃ (3.0 × 108 sec)

0.03 |λα1| 2 0.04 |λ′

α13|

4 mX 1 TeV 6 .

Constraint from n − ¯ n

100 200 500 1000 2000 5000 0.001 0.010 0.100 1 mX (GeV) |λ13  | τnnb < 3 x 1 08 s e c < 5 x 1 010 s e c

There is a lower limit on |λ′

13| 10−11 requiring that X decay temperature

is above QCD scale. But the corresponding upper limit on τn¯

n is useless (1062 sec).

Constraint from n − ¯ n

100 200 500 1000 2000 5000 0.001 0.010 0.100 1 mX (GeV) |λ13  | τnnb < 3 x 1 08 s e c < 5 x 1 010 s e c

There is a lower limit on |λ′

13| 10−11 requiring that X decay temperature

is above QCD scale. But the corresponding upper limit on τn¯

n is useless (1062 sec).

Collider Signals

λ1 λ2 d d0 ¯ u nDM X∗ nDM ¯ u ¯ d0 d g d0

DM production pp → ψuc gives a monojet (monotop for λα3) signal. For λ′

13,23, the quark annihilation must involve the b-quark PDF (small).

Another way: gluon splitting into b¯ b. Extra b can be used for event tagging. The color-triplet scalar will also give a dijet resonance at the LHC.

d d0 d d0 λ1 λ1 X∗

Monojet

Different from other DM production at the LHC: pp → DM DM. Will give a Jacobian peak in the jet pT distribution. [Duta, Gao, Kamon (PRD ’14)]

100 200 300 400 500 600 700 10-5 10-4 10-3 jet PT @GeVD dsêdPT @pbêGeVD LHC 8 TeV M X1 2

PT >450 GeV

n¯ n - LHC Complementarity

100 200 500 1000 2000 5000 10-4 0.001 0.010 0.100 1 mX (GeV) |λ13  | τ

n n b

< 3 x 1

8

s < 5 x 1

1

s m

• n
• j

e t ( 8 T e V ) monojet (13 TeV)

Conclusion

A simple TeV-scale model of B-violation for baryogenesis and dark matter. Stability of dark matter linked to that of proton (no ad-hoc symmetry required). DM-to-baryon abundance ratio easily explained. Imposes an upper limit on the coupling ratio |λ/λ′|. Successful baryogenesis imposes a lower bound on |λ/λ′|. Potentially observable n − ¯ n oscillation rate. No EDM constraints. Distinct monojet and dijet signatures at the LHC. Complementarity between monojet and n − ¯ n.